Solve 20/65*100/308div55/44+5/26=?

$$\frac { 20 } { 65 } \times \frac { 100 } { 308 } \div \frac { 55 } { 44 } + \frac { 5 } { 26 } = ?$$

Evaluate

$$\frac{545}{2002}\approx 0.272227772$$

Solution Steps

Reduce the fraction \frac{20}{65} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{4}{13}\times \frac{100}{308}}{\frac{55}{44}}+\frac{5}{26}$$

Reduce the fraction \frac{100}{308} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{4}{13}\times \frac{25}{77}}{\frac{55}{44}}+\frac{5}{26}$$

Multiply \frac{4}{13} times \frac{25}{77} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 25}{13\times 77}}{\frac{55}{44}}+\frac{5}{26}$$

Do the multiplications in the fraction \frac{4\times 25}{13\times 77}.

$$\frac{\frac{100}{1001}}{\frac{55}{44}}+\frac{5}{26}$$

Reduce the fraction \frac{55}{44} to lowest terms by extracting and canceling out 11.

$$\frac{\frac{100}{1001}}{\frac{5}{4}}+\frac{5}{26}$$

Divide \frac{100}{1001} by \frac{5}{4} by multiplying \frac{100}{1001} by the reciprocal of \frac{5}{4}.

$$\frac{100}{1001}\times \frac{4}{5}+\frac{5}{26}$$

Multiply \frac{100}{1001} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{100\times 4}{1001\times 5}+\frac{5}{26}$$

Do the multiplications in the fraction \frac{100\times 4}{1001\times 5}.

$$\frac{400}{5005}+\frac{5}{26}$$

Reduce the fraction \frac{400}{5005} to lowest terms by extracting and canceling out 5.

$$\frac{80}{1001}+\frac{5}{26}$$

Least common multiple of 1001 and 26 is 2002. Convert \frac{80}{1001} and \frac{5}{26} to fractions with denominator 2002.

$$\frac{160}{2002}+\frac{385}{2002}$$

Since \frac{160}{2002} and \frac{385}{2002} have the same denominator, add them by adding their numerators.

$$\frac{160+385}{2002}$$

Add 160 and 385 to get 545.

$$\frac{545}{2002}$$

Factor

$$\frac{5 \cdot 109}{2 \cdot 7 \cdot 11 \cdot 13} = 0.2722277722277722$$